f you were allowed an infinite amount of time to run every possibilty in step-by-step fashion. But can you assume you will be afforded the luxury of time?...

Nonsense. You may not have much time, but that doesn't mean you automatically won't be able to exercise a modicum of good judgment. The fundamental error, that can doom one to failure, is the entrenched belief that the only appropriate response is to charge in to the rescue with guns blazing.